Question: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{k^2 - 5k}{k^2 - 11k + 30}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 - 5k}{k^2 - 11k + 30} = \dfrac{(k)(k - 5)}{(k - 6)(k - 5)} $ Notice that the term $(k - 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k - 5)$ gives: $y = \dfrac{k}{k - 6}$ Since we divided by $(k - 5)$, $k \neq 5$. $y = \dfrac{k}{k - 6}; \space k \neq 5$